列方程解应的用题专练

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᪆௃Æ⚪ᑖ᪆¹1,8ᜧøùxúᑣCøùᨵ¹20-x,úü±ᜧCøùᐳþ240ᔴṺᑡᓽ2᣸10AᙢᐸAᙢḄᜧᨵ4ᑣ$ᨵ10-a'(1Ḅ)*+,-.BᙢḄᜧஹ$Ḅᦪᑖ345ᔜ7Ḅ)8ᓽ9:)8.<⚪ᑖ᪆?1@ᜧxᑣ$ᨵ20-x15x+1020-x=240,-?x=8,$ᦪ9?20-x=20-8=12ᦑᜧᵨ8$ᵨ122•.•AᙢḄᜧᨵaKᫀM6⚓:18⚓

12...ᑮAᙢḄ$ᨵ(10-a),ᑮBᙢḄᜧ(8-a),ᑮBᙢḄ$ᨵj12-(10-a)k=(2+a)lW=630a+420(10-a)+750(8-a)+550(2+a)=630a+4200-420a+6000-750a+1100+550a=10a+U300ᦑWraḄᐵtu9W=10a+11300.ὃv?1.wᐗwyḄzᵨ2.wy{ᦪ.ூKᫀ௃(1)|}.Ḅ~☢ᦪ96x+4(19-x)=(2x+76)|}.Ḅ☢ᦪ95(19-x)=(-5x+95)(2)ᨬ5Ḅᦪ930ூ
᪆௃<⚪ᑖ᪆?(1)XᵨA-~☢ᦪ96Xᑣ(19-X)ᵨB-~☢ᦪ94(19-X)-5(19-X)(2)~☢r☢ᡂw<⚪᪆?(1)|}.Ḅ~☢ᦪ96x+4(19-x)=(2x+76)|}.Ḅ☢ᦪ95(19-x)=(-5x+95)(2)ᵫ⚪-.2x+76-5x+95.X=7ᨬ5Ḅᦪ930ὃv?1ஹᵨᦪu⊤2ஹᝅ⚪25.6ḄOᨬூ
᪆௃ᫀᔠᳮḄ⚪¢ᡃ¤5ᑖ3¥*.¦ᦟ¨©ªḄO«¬®஺1)@¯ᐭw6ḄO«XᐗX(1+6X2.88%)=20000,X=170532)@¯ᐭ²³ḄO9YᐗY(1+2.7%X3)(1+2.7%X3)=20000,X=171153)@¯ᐭwO9ZᐗZ(1+2.25%)e=20000,Z=17894ᡠ5¯ᐭw6ḄOᨬ஺26.2.16%ூ
᪆௃¸¹ᐵt?Oº»=OX(1+ᑭ᳛)@¾Ḅ¿▭ᑭ᳛9X,250(1+X)=252.7X=0.0108ᡠ5ᑭ᳛90.0108X2=0.0216K?Á®Ḅᑭ᳛«2.16%27.37.5ᓟÃூ
᪆௃kÄÅ⚪ÆÇÈÉ.ÊḄ:ËÌÍÉḄ⚪ÎᓄᡂᵬÑÒḄÄÅ⚪஺KᫀM7⚓:18⚓

13ÊÓḄ:Ë=ÔḄÕÖX×ÍØÔᵨḄ:×ÍÙ«ᵬÄÚÑḄ×Í@ᵬᵨX$×ÄÚÑ᪷(⚪ᑡ5X=3X+5-X=2.5,ÊḄ:Ë?15X2.5=37.5K?ÊḄ:Ë«37.5ᓟÃ஺4028.9ூ
᪆௃ᵬÜÝ10ᜩßᡂàáḄâḄãÝᦔ᳛«1/10,ÑḄãÝᦔ᳛«1/8¸¹ᐵt«?ᵬÑᔠÝḄᦔ᳛XᔠÝḄ×Í=1@ᔠÝXᜩßᡂ40(1/10+1/8)X=1-X=940K?ÒᔠÝ9ᜩßᡂ29.113.ூ
᪆௃I7_1Q<⚪ᑖ᪆?@$UᡂᕒᐳᨵXèᵫ⚪ᑡ.érã==r2,ᓽ.65I7_1Qrr<⚪᪆?@ê$U¥ᑜX“í+”ᑣï•=—2,-X=U3,ᦑê$U¥65ᑜ113“í+”.ὃv?wᐗwyḄzᵨ.30.ñYÒᦪ«270Òᓫó45ôõ◤6ூ
᪆௃<⚪ᑖ᪆?÷ᑮ¸¹ᐵt?ñYÒᦪÆøᑡ..<⚪᪆??@óᵨ45ôḄõxᑣóᵨ60ôõ(x—l)ᵫ⚪ᑡ.945x=60(x-1)-30-=6஺ᡠ5dú᧡üÒᦪ945X6=270(Ò).K?᜜.þüḄñYÒᦪ«270Òᓫó45ôõ◤6.ὃv?wᐗwyḄzᵨ31.(1)ÿ0VxW82.2xᐗx>82.9x-5.6ᐗ(2)23.4ᐗூ
᪆௃⚪ᑖ᪆(1)᪷ᑴ"#$%ᵨ᪗()ᡝ)ᨴᵨ,-.8/01ஹ)/01ᦈ2.00ᐗ,56ᦈ0.20ᐗ//01Ḅ9:;ᜐᳮ;-.8/01Ḅ?ᑖ)/01ᦈ2.50ᐗ56ᦈ0.40ᐗ//01Ḅ9:;ᜐᳮᡠ$⌕ᑖ08CDᓽF(2)GHI10ᨴJᵨ10/01Kx>8,LMᐭ2.9x-5.6OPIQRᨴḄS⚪T᪆Tপ088X2.2+(2.5+0.4)(x-8)=2.9x-5.6ᐗফx=102.9X10-5.6=23.4ᐗ.Zᫀ\8⚓^18⚓

14ὃx1.ᑡMᦪ{2.OMᦪ{Ḅ|7132.(1)5(2)—ᡈ—.23ூ
᪆௃⚪ᑖ᪆(1).xxMxN54RᓫᵫxMAx)2RᓫxNxBMxḄ3,2x+6x+14=54OᓽF(2)✌ᐜ.xxPᑮxM,NḄ(2t+6)-t=(6t-8)-tᡈ(2t+6)-t=t-(6t-8),OᓽF.⚪T᪆(1).xxMxN54Rᓫ.⚪Fᑡ02x+6x+14=54,T0x=5.Z.5xMxN54Rᓫ.(0¡pL¢ᑖ)(2).txPᑮxM,NḄ.(2f+6)—f=(6f—8)—fᡈ(2f+6)-f=f-(6f-8),71f+6=5f-8ᡈ£+6=8-5/,Tt='ᡈf=¦2371Z.§ᡈ§xPᑮxM,NḄ.23ὃx1.§ᐗ§¨0ḄLᵨ2.ᦪ©.33.Gªᢗ3R3ᑖᳫ7R2ᑖᳫ.ூ
᪆௃ᐵ¯জ3ᑖᳫḄ^ᑖᦪ+2ᑖᦪḄ^ᑖᦪ=23;ঝ2ᑖᳫᦪ-3ᑖᳫᦪ=4.TᢗḄ3ᑖᳫxRᑣᢗḄ2ᑖᳫ(x+4)R3x+2(x+4)=23,Tx=3,x+4=7.ZGªᢗ3R3ᑖᳫ7R2ᑖᳫ.34.400ᓟ´ூ
᪆௃_⚪Ḅᐵµ¶K“¸6”ºKᙠ»ᨵxᓟ´Ḅ½Ạ¦¿À7.5ÁÂûÄḄ(1+7.5)#.T◤⌕xᓟ´ÆÇᑣ(1+7.5)x=3400,Tx=400.Z◤⌕400ᓟ´ḄÆÇ.35.5Èூ
᪆௃TxÈq᱄ÊḄÈËKÌÍÈËḄ2.5᪷⚪40+x=2.5(x+13)TQR0x=5.Z5Èq᱄ÊḄÈËKÌÍÈËḄ2.5.36.ᨵ3RGÎ,4RÏ.ூ
᪆௃TᨵxRGÎ,᪷⚪,x+l=2x—2,TQR0x=3.x=3,x+l=3+l=4.Z:ᨵ3RGÎ,4RÏ.37.32ூT᪆௃ᐵ¯GÒÓ+400=ÔÔÓxÕÖ✌¨⍗Zᫀ\9⚓^18⚓

155x+7.5x=400x=32Z32ÕÖ✌¨⍗ூZᫀ௃83ᑖூT᪆௃Øᙳᑖ=^ᡂÚ/ÖᦪØᙳᡂÚKxᑖ40*87.l+42x=85*823484+42x=697042x=3486x=83ZØᙳᡂÚK83ᑖூZᫀ௃40ᓟ1ூT᪆௃Ó=xÜᐵ¯^Ó=ᵬÞÓ+ßÞÓ+17ß)Gàxᓟ13(45+x)+17=2723(45+x)=25545+x=85x=40ß)Gà40ᓟ13340.áᡈ45ூT᪆௃⚪ᑖ᪆ᵫ⚪Fâ!ä஺ä1\§¨åæqᒕ%ḄèéḄêa,ì1-஺2ᡠ$\í¨åæî0éḄïê1-4,\í¨åæ$qᒕ%ḄèéḄÕïᑖð1-4,22a-l.ñᑖÕòóôজ᝞ö1—஺÷2஺§1,ᓽ“ä§øù\ú¨åæî0éḄ3ïê2஺-1.•.•.\ú¨åæqᡠḄèéKî0é,èéḄìü1—a,3ᓽ2஺§1=(1§஺)§(2஺§1),T஺=ý2ঝ᝞ö1§஺ä2஺§1,ᓽ஺÷úøù\ú¨åæî0éḄïêl-a.33þLil-a=(2a-1)-(1-a),a=—.433ᦑᫀᡈ.45ὃ1.ᐗḄ!ᵨ#2.$%&.41.Dூ᪆௃+⚪ᑖ᪆.1ᐗ/0x23455ᐗ/0ᨵ(12-x)23#.x+5(12-x)=48,ᦑ⌱D.ὃᑡᐗ.42.(1)15;#(2)2<#(3)=>15;.ᫀ?10⚓3A18⚓

16ூ
᪆௃+⚪ᑖ᪆(1)Xk=0.1,t=0.5,v=10]ᐭᓽ`ᑮᑷcde;(2)Xk=0.1,v=15,s=52.5]ᐭᡠijᦪ`tḄl;(3)Xv=10,t=0.5,k=0.1]ᐭs=tv+kv?nosḄlᓽ`.+⚪᪆:পXk=0.1.t=0.5,v=10]ᐭs=tv+kv?ns=0.5X10+0.1X1O2=15#ᦑᫀ15(2)Xv=15,s=52.5,k=0.1]ᐭs=tv+kv'n52.5=15t+0.1X15?,t=2,(3)Xv=10,t=2,k=0.1]ᐭs=tv+k/ns=10X2+0.1X10=30,Xv=10,t=0.5,k=0.1]ᐭs=tv+kv?ns=10X0.5+0.1X102=15,30-15=15,ᦑᫀ2#30#15.ὃᐗḄ!ᵨ.9143.(1)(-x-30)v.(2)(-x+50)v.55ூ
᪆௃4+⚪ᑖ᪆(1)᪷x?ycz{?czvᦪḄ|}30vᓽ`⊤?yczḄvᦪ#5(2)?yczo10v3ᑣ?ycz}10v3?cz10v.ᑖ⊤oczḄvᦪR.44+⚪᪆(1)•••?ycz{?czvᦪḄ}30v3.•.?yczᨵ(x-30)v.5549ᑣczᐳᨵx+(-x-30)=(-x-30)v.554(2)(x+10)-(-X-30-10)54=x+10--x+30+105=x+505.•.?czḄvᦪ{?ycz(!x+50)v.5ὃᑡ]ᦪ.44.᪆ூ᪆௃⚪⌕ὃ⇋XḄ஺.AᵨYᐗ3X2ᵯᾯYi=8X¡᪥¢=4X+120£X=30¤3¥¦¥2£X>30¤3YAY2£XV30¤,YI

17ூ
᪆௃+⚪ᑖ᪆¸¹ᙳ»ᔴ1.4ᐗᜧ¾1.2ᐗ3¿Bᨴᵨ¸ÁÂÃ6ᔴ345᪗ÆᑁḄ¸>|ÁoÈᑖÉÊË▭¸.᪷xÍÎÏᐵÑᑡoÒ.+⚪᪆.Óᵨᡝ5ᨴÕË▭ᵨ¸xᔴ3ᑣ1.2x6+(x-6)x2=1.4x,7.2+2x-12=1.4x,0.6x=4.8,x=8.Óᵨᡝ5ᨴÕË▭ᵨ¸8ᔴ.ὃᐗḄ!ᵨ.3347.'ᡈ54ூ
᪆௃+⚪ᑖ᪆ᵫ¾»$%¤ᡠÖ×ḄØÙÚξÛÜ×ḄÝ3ᑣ?$%¤3Þß-2஺-1¤3ᓽa<—¤33ᑣ?$%ᡠḄÖ×ḄØÙ2a-1,ᒕâḄÜ×Øᑖ-1ஹ1—ci—(2a-1)=2-3஻3,**2஺—1=2—3a,._3••a——.52£1—Q<2cl—1¤3ᓽ—¤33ᑣ?$%ᡠḄÖ×ḄØÙ3ᒕâḄÜ×Øᑖஹ2஻-1—(1-Q)=3d—2,,•*1—ci=3஺—29.a=~.433ᦑᫀñᡈñ.54ὃ1.òᢚôᣚ(ᢚö÷⚪)#2.ø/÷⚪.48.D.ூ
᪆௃+⚪ᑖ᪆Þßù(19)ûᨵ48üý¡3ᑣþ¡Kᦪ24,᪷x1ÿ3=2+1ᡭᵯ24=2+2ᡭᵯ35=2+3ᡭᵯ…24=2+஻ᡭᵯᓽ.ᫀ12⚓18⚓

18•.•<(19)=ᨵ48,...,ᦪA24,VI3=2+1ᡭᵯ24=2+2ᡭᵯ35=2+3ᡭᵯ…஻24=2+”ᡭᵯ஻=22,ᑣC=᝕ḄFᦪG48-22=26Fᦑ⌱I).ὃJKLᵨMN⚪.49.Aூ
᪆௃P⚪ᑖ᪆Kᡂ!SAxᐗᢥᡂ!SVW30%3᪗S᪗SAKx•(1+30%),᪗SḄ80%├ZZSAKx(1+30%)X80%,ᡠ\⌱A.ὃJKᐗ]^_`Lᵨ50.(1)a=60.(2)Cᡝbᨴdᐳᵨᵯ90fLgᵯh32.40ᐗ.ூ
᪆௃i!ᦪjᐵlGKᵯh=ᵨᵯjXmfᵯS.!⚪⌕opKqrafsᑖḄᵨᵯjᐸᵯSuaf\af\ᑁḄᵨᵯjḄᵯSw.K(1)ᵫ⚪pᨵy᪵Ḅ{|ᐵlKafᵯḄᵯh+qrafḄ}sᑖᵯh=~ᨴdᵯhᵫ`^_0.40a+(84-a)X0.40X70%=30.72,`a=60.(2)Cᡝbᨴdᐳᵨᵯxfᵫ⚪pᨵ{|ᐵlK60fᵯḄᵯh+qr60fḄ}sᑖᵯh=bᨴdᵯhᵫ`^_0.40X60+(x-60)X0.40X70%=0.36x,`x=90,ᑣ0.36x=32.40.KCᡝbᨴdᐳᵨᵯ90fLgᵯh32.40ᐗ.51.50000ᓟூ᪆௃⚪rᐵ“ᒕ”`r!⚪ḄᦻḄ|jᐵl“ᨵḄrḄ=ᒕḄ”ᳮ.Kᩭᨵxᓟ☢}r15%xᓟᵫ⚪p`x—15%x=42500,^_xx=42500,100ᡠ\x=50000.Kᩭᨵ50000ᓟ☢.52.200ᐗூ
᪆௃|jᐵlKZS=S+SXᑭ᳛KyᢇḄSGxᐗᑣX+40%x=280`x=200KyᢇḄSG200ᐗ53.¡¢£q¤ḄᢚᡷG§ᢚ.ூ
᪆௃P⚪ᑖ᪆Kᡭᢚ¨AᖪªḄᓫSGxᐗBᖪªḄᓫSGyᐗ᪷ᡭᢚ¨®¯5°Aᖪª±1°Bᖪª◤ᵨ84ᐗ³®¯6°Aᖪª±3°Bᖪª◤ᵨ108ᐗᑡ^_'.ᫀ13⚓18⚓

19P⚪᪆Kᡭᢚ¨AᖪªḄᓫSGxᐗBᖪªḄᓫSGyᐗ,5x+y=84ᵫ⚪p`:6x+3y=108x=16`:y=4ºij3x+8y=3X16+8X4=80(ᐗ)¡¢£q¤ḄᢚᡷAK72+80=90%.K¡¢£q¤ḄᢚᡷG§ᢚ.ὃJKÅᐗ]^_'ḄLᵨ.ூᫀ௃(1)360³(2)ᖪBூ᪆௃ÆᒹḄSÈGxᐗᑣᵫ⚪p`ÉÊËḄSÈA(4x-8)ᐗᑣᨵ:4x-8+x=4525x=460x=92ᡠ\K4x-8=4X92-8=360ᖪA:452X8096=361.6ᖪB452-(4X25)=352ÍA361.6>352ᡠ\ᙠᖪB®¯ÏᔠÑ஺55.B.ூ᪆௃P⚪ᑖ᪆K⌕ᑡ^_✌ᐜ⌕᪷⚪prÔᙠḄ|jᐵl!⚪᪷“ÕÖᢥSᡭ8ᢚrZᙊØÖᢥSᡭ9ᢚrZÙÚÛÖᐳᓬr60Ýᓬ`Þß87ᐗ”`r|jᐵlKxÝÕÖḄZS+(60-x)ÝᙊØÖḄZS=87,ᑡr^_K1.2X0.8x+2X0.9(60-x)=87.ᦑ⌱BὃJKᵫà▭N⚪âãrᐗ]^_(├ZN⚪).56.20%.ூ᪆௃ᦪjᐵl᝞å⊤Kçèᨴyèᨴéêëj11-5%ëéêhᵨ11+14%éêSÈ11+xyèᨴḄéêSÈ{2çèᨴḄìí᳛AX.᪷⚪p`K(1+x)(1-5%)=1+14%`x=1/5=20%KyèᨴḄéêSÈ{2çèᨴḄìí᳛A20%.ï᪆Kðñ⊤Èᩭᑖ᪆òóᩖḄᦪjᐵl.y⍝⚪ᡠᵨḄ{|ᐵlGKᦪjXSÈ=hᵨ.57.30ᐗ.ூ᪆௃yᢇöᱥḄZSAxᐗᑣᵬḄùúG(x-10)X10%ᐗûḄùúG(x-ᫀ14⚓18⚓

20yᢇöᱥḄZSAxᐗ᪷⚪p`K(x-10)*10%=(x-20)X20%ᓄþ`KX—10=2(X—20)ᓽx-10=2x-40x=30ᢇᱥḄ30ᐗ.58.65ᐗ84ᐗூ᪆௃$%ᑡ⊤ᑖ᪆)*ᩩ,-ᑮ/0ᐵ234ᢚᡷ᳛᪗9:ᑭ<᳛60ᐗ8ᢚXᐗ80%x40%/0ᐵ2ᖪ?ᑭ<᳛=ᖪ?ᑭ

21ABLVvxOPQzALS⍗᪷|⚪hᑡbY50x+30x=240x=3ABLVv3OPQzALS⍗஺63.3000.ூ
᪆௃I⚪ᑖ᪆eᑖRbcgBAOp%xᑖnstOu|⚪hᑡbYcᵬஹ¡RᙢḄXY£¤B¥¦Aᵬ¡RᙢḄXYy[ᑡbYcᓽe.bgAOp%xᑖnstOeᑡbY250x=3X200+200x,x=12,XY:250X12=3000[£b¤Aᵬ¡RᙢḄXYy[eᑡbY__=?20250'y=3000,ᦑᵬஹ¡RᙢC¬ḄXYB3000[.ὃjgᐗgkbYḄlᵨ.64.125ᐗூ
᪆௃®V°⚪±°⚪²⌕³´(1)µ¶·¸=ᙠ☟¶²Ḅ·¸+¶º·¸£(2)⌮¶·¸=ᙠ☟¶²Ḅ·¸g¶º·¸஺S/ᐵ2µº¼VḄP¬+⌮º¼VḄP¬=7OP஺AAஹBRṹᜮC¬Ḅ¼Yxᓟ[ᑣBஹC¬Ḅ¼Y(x—10)ᓟ[ᵫ⚪hX/(8+2)+(X-10)/(8-2)=7ÁbYX/10+(X-10)/6=7,x=32.5AஹBRᙢC¬ḄXY32.5ᓟ[஺.16121—65.(1)23(2)23(3)2.4(4)9.6(5)11.4ூ
᪆௃Â⚪ᐵÃB⌕ᳮ´ÅSᔣஹSÇஹÈᔣ/ḄÉʳ´VW%Y஺ᦑeËᔠÍÎᑖ᪆஺(1)S⍗°⚪ÏÍ⊤Ðk------z----------yÑஹᵬ¡/0ᐵ2B᠒LÒḄXY+KLÒḄXY=480ÓÔ஺AKLMNxOPQRLS⍗Õ⚪h140x+90(x+l)=480ÁbY230x=390וx=23••AKLMN23OPRLS⍗ᫀ16⚓18⚓

22(2)SÇÙVÏÍ⊤Ð:600_/0ᐵ2BRLᡠÒḄXY+480ÓÔ=600ÓÔ஺AxOPQRLSy600ÓÔᵫ⚪h(140+90)x+480=600ÁbY230x=1201223OPQRLSy600ÓÔ஺(3)/0ᐵ2KLᡠÒXYg᠒LᡠÒXY+480ÓÔ=600ÓÔ஺AxOPQRLSy600ÓÔᵫ⚪h(140-90)x+480-60050x=120/.x=2.42.4OPQRLSy600ÓÔ஺(4)sÛ°⚪ÏÍ⊤Ð/0ᐵ2KLḄXY=᠒LÒḄXY+480ÓÔ஺AxOPQKLst᠒L஺ᵫ⚪h140x=90x+480ÁbY50x=480x=9.69.6OPQKLst᠒L஺(5)sÛ°⚪/0ᐵ2KLḄXY=᠒LÒḄXY+480ÓÔ஺AKLMNxOPQst᠒L஺Õ⚪h140x=90(x+1)+48050x=570x=11.4KLMNIL4OPQst᠒L஺6஺66.5ூ᪆௃AÞY0ᓫà1,/0ᐵ2ᵬáᡂÞâ0+¡áᡂÞâ0=Þâ0஺A¡ã◤xᜩáᡂᐰçÞYAÞâ0ᓫà1,Õ⚪h(1$+12)X3+12=1,ᫀ17⚓18⚓

23¡ã◤5ᜩrèáᡂᐰçÞY஺ᫀ18⚓18⚓